We present a streaming algorithm for constructing a coreset for metric \(k\) -means clustering that requires the storage of \(O(\epsilon ^{-2} k \log n)\)  points. The previous state-of-the-art [1]} required the storage of \(O(\epsilon ^{-4} k \log k \log ^6 n)\)  points. In this section we assume the correctness of our offline algorithm, which is proven in Section .
